Question:
Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the following sets are functions from X to Y.
(a) f1 = {(1, 1), (2, 11), (3, 1), (4, 15)}
(b) f2 = {(1, 1), (2, 7), (3, 5)}
(c) f3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}
Solution:
(a) Given:
f1 = {(1, 1), (2, 11), (3, 1), (4, 15)}
f1 is a function from X to Y.
(b) Given:
f2 = {(1, 1), (2, 7), (3, 5)}
f2 is not a function from X to Y because 2 ∈ X has no image in Y.
(c) Given:
f3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}
f3 is not a function from X to Y because 2 ∈ X has two images, 9 and 11, in Y.
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